### VIASM Annual meeting 2012

Time:13:30:25/08/2012 to  17:00:26/08/2012

Venue/Location: Lecture hall C2, Vietnam Institute for Advance Study in Mathematics (VIASM) 7-th floor, Ta Quang Buu Library, Hanoi University of Science & Technology

Organisers: Prof. Ngo Bao Chau (Univ. of Chicago & VIASM) and Prof. Phung Ho Hai (Institute of Mathematics, Hanoi)

Invited Speakers: Prof. Dinh Tien Cuong, Univ. Paris 6, France; Prof. Jean-Pierre Demailly, Univ. Grenoble, France; Prof. Hélène Esnault, Univ. Duisburg-Essen, Germany; Prof. Benedict Gross, Univ. Harvard, USA; Prof. Lionel Schwartz, Univ. Paris 13, France

Content:

Venue: Lecture hall C2, Vietnam Institute for Advance Study in Mathematics (VIASM)

7-th floor, Ta Quang Buu Library, Hanoi University of Science & Technology

Organizers: Prof. Ngo Bao Chau (Univ. of Chicago — VIASM) and Prof. Phung Ho Hai (Institute of Mathematics, Hanoi)

“VIASM Annual meeting” is an official activity of Vietnam Institute for Advance Study in Mathematics.

VIASM will invite highly reputed mathematicians to deliver lectures on central topics of contemporary mathematics. The lecturers will provide the audience with problems of high interest in their research fields, main ideas and main results. The lectures will be published in a special issue of Acta Mathematica Vietnamica.

The following scientists have agreed to deliver their lectures at VIASM Annual Meeting 2012

Prof. Dinh Tien Cuong, Univ. Paris 6, France

Prof. Jean-Pierre Demailly, Univ. Grenoble, France

Prof. Hélène Esnault, Univ. Duisburg-Essen, Germany

Prof. Benedict Gross, Univ. Harvard, USA

Prof. Lionel Schwartz, Univ. Paris 13, France

Registration:

VIASM cordially invites all interested colleagues to participate VIASM Annual Meeting 2012. The will be no conference fee. For the registration please send an email to VIASM at the following address:

To: application@viasm.edu.vn or info@viasm.edu.vn

Subject: Viasm AM – 2012

Form

Lecture content

Jean-Pierre Demailly: Hyperbolic algebraic varieties and holomorphic differential equations

Every complex space carries an invariant metric known as the Kobayashi metric, computed from extremal holomorphic curves. On projective varieties, Kobayashi hyperbolicity is equivalent to the non existence of entire holomorphic curves. In general it is expected that the existence of infinitely many rational points is related to the locus where entire holomorphic curves accumulate. An important conjecture due to Green-Griffiths and Lang asserts that for every projective algebraic variety of general type, there is a proper algebraic subvariety containing all entire curves, that would contain also all rational points but finitely many. The description of this locus is strongly related to certain global algebraic differential equations, given e.g. by holomorphic foliations. The geometry of jet bundles and their cohomology plays here an important role. We will discuss recent progress on these questions.

Hélène Esnault: Finiteness and companions, after P. Deligne and V. Drinfeld

Goal will be to present Deligne’s existence of a number field receiving the coefficients of an $\ell$-adic lisse sheaf of weight 0 on a normal scheme $X$ over a finite field, Drinfeld’s existence of $\ell’$-adic companions on $X$ lisse (Deligne’s conjecture1.2.10 in Weil II), and Deligne’s finiteness result for the number of $\ell$-adic lisse sheaves to bounded rank and ramification.

Benedict Gross: On the arithmetic of hyperelliptic curves

In this talk, I will show how one can use invariant theory to study the arithmetic of hyperelliptic curves of a fixed genus over Q with a rational Weierstrass point. I will obtain an upper bound on the average rank of their Jacobians and will use this bound to restrict the number of rational points on the curve (when the genus is at least 2). This
is a report on joint work with Manjul Bhargava.

Dinh Tien Cuong: Automorphism groups of compact Kaehler manifolds

Automorphisms of compact Kaehler manifolds are currently studied mostly from two points of view: Complex Dynamics and Algebraic Geometry. In this talk, we will survey some classical results, e.g. Theorems by Lieberman, Gromov, Yomdin, and some recent progresses, e.g. a version of Tit’s alternative obtained by D.-Q. Zhang.

Lionel Schwartz: Realizing unstable modules as the cohomology of spaces, a survey

The talk will describe recent results and conjectures about the following question: when an unstable module can be the mod p cohomology of a space. One will focus on qualitative results (but not only) rather than on specific cases.

Financial support: VIASM would provide full accommodation and partial travel expenses for a number of young scientists, graduate students who are not from Hanoi to participate the Annual Meeting. To apply for the financial support please send an application form together with a scientific CV to VIASM at the email addresses mentioned above.

Program

Saturday, August 25, 2012

- 13h30-14h15: Tea

- 14h15-15h45: Lecture “On the arithmetic of hyperelliptic curves” presented by Professor Benedict Gross

- 15h45-16h00: Tea

- 16h00-17h30: Lecture “Automorphism groups of compact Kaehler manifolds” presented by Professor Đinh Tiến Cường.

Sunday, August 26, 2012

Morning

- 8h30-8h45: Tea

- 8h45-10h15: Lecture “Finiteness and companions, after P. Deligne and V. Drinfeld” presented by Professor Hélène Esnault

- 10h15-10h30: Tea

- 10h30-12h00: Lecture “Realizing unstable modules as the cohomology of spaces, a survey” presented by Professor Lionel Schwartz.

Afternoon

- 14h00-14h15: Tea

- 14h15-15h45: Lecture “Hyperbolic algebraic varieties and holomorphic differential equations” presented by Professor Jean-Pierre Demailly

- 15h45-16h00: Tea

- 16h00: Round table discussion on the next meeting